According to the Landau theory of phase transitions, the superconducting gap functions are classified according to single-valued irreducible representations (irreps) \(\gamma \)  of the point group \(\mathbb {G}\) ,
called the pairing channels. In a \(d\) -dimensional pairing channel, the singlet gap function can be represented in the form \(\psi ( {k} )=\sum _{a=1}^{d}\eta _a\varphi _a( {k} )\) ,
where \(a\)  labels the scalar basis functions \(\varphi \)  of an even irrep \(\gamma \) . Similarly, the triplet gap function can be represented as \( {d} ( {k} )=\sum _{a=1}^{d}\eta _a{\varphi }_a( {k} )\) ,
where the basis functions \({\varphi }\)  of an odd irrep \(\gamma \)  have different form in the pseudospin and non-pseudospin bands, see Ref. Sam19-PRB.
In both singlet and triplet cases, the components of the superconducting order parameter \(\eta _1,..,\eta _d\)  are found by minimizing the free energy of the superconductor.[1]}, [2]}
The point group \(\mathbf {D}_6\)  has four one-dimensional (1D) irreps \(A_1\) , \(A_2\) , \(B_1\) , \(B_2\) , and two 2D irreps \(E_1\) , \(E_2\)  (we use the “chemical” notation[3]} for the pairing channels,
reserving the \(\Gamma \)  notation[4]} for the double-valued coreps describing the symmetry of the Bloch bands). Taking into account the parity, there are six singlet and six triplet pairing channels.
